PUC Science 2nd PUC Class 12 - Karnataka Board PUC Question Bank Solutions for Mathematics

Evaluate the following integral:

Write a value of

Write a value of

Evaluate:\[\int\frac{x^2}{1 + x^3} \text{ dx }\] .

Evaluate:

Evaluate:\[\int\frac{\sec^2 \sqrt{x}}{\sqrt{x}} \text{ dx }\]

Evaluate:\[\int\frac{\sin \sqrt{x}}{\sqrt{x}} \text{ dx }\]

Evaluate:\[\int\frac{\cos \sqrt{x}}{\sqrt{x}} \text{ dx }\]

Evaluate:\[\int\frac{\left( 1 + \log x \right)^2}{x} \text{   dx }\]

Evaluate:\[\int \sec^2 \left( 7 - 4x \right) \text{ dx }\]

Evaluate:\[\int\frac{\log x}{x} \text{ dx }\]

Evaluate:  \[\int 2^x  \text{ dx }\]

Evaluate: \[\int\frac{x^3 - x^2 + x - 1}{x - 1} \text{ dx }\]

Evaluate:\[\int\frac{e\tan^{- 1} x}{1 + x^2} \text{ dx }\]

Evaluate: \[\int\frac{1}{\sqrt{1 - x^2}} \text{ dx }\]

Write the value of\[\int\sec x \left( \sec x + \tan x \right)\text{  dx }\]

Evaluate: \[\int\frac{1}{x^2 + 16}\text{ dx }\]

Evaluate: \[\int\left( 1 - x \right)\sqrt{x}\text{  dx }\]